Kapitel 5

Question 1

Long Run Costs

Answer 1

• all inputs can be adjusted
• relationship between cost function and returns of scale of technology is possible

Question 2

Long Run Costs Cobb Douglas Minimization

Answer 2

• aim: isocost=isoquant

Question 3

Long Run Costs Linear Minimization

Answer 3

Question 4

Long Run Costs Leontief technology minimization

Answer 4

Question 5

Long Run Cost Function

Answer 5

• similiar to expenditure function
  properties:
• increasing in y and non-decreasing in p
• linear homogeneous in p
• concave in p
• shepards lemma: Ableitung von c nach pi= zi(p,y)
• lagrange multiplier gives long-run marginal cost of output (LRMC)

Question 6

Long run cost function: Output level and input choice

Answer 6

• If output y increases, the optimal cost-minimizing input choice changes.
• The expansion path EP is the locus of optimal input combinations for varying output y with input prices held constant.
• The EP can have a positive and over some range also a negative slope.
• If the required amount of an input increases for increasing output, this input is normal.
• If the required amount of an input decreases for increasing output, this input is inferior or regressive.
• If the production function is homothetic input proportions are the same at all output levels.
• The EP will be a ray from the origin.
• Only changes in relative input prices cause changes in input proportions.

Question 7

Long run marginal cost

Answer 7

Ableitung der Kostenfunktion nach y

Question 8

Long Run Average cost

Answer 8

LAC= Kostenfunktion durch y teilen

Question 9

Long Run costs: Economies of scale and returns

Answer 9

Question 10

Long run costs: Homotheticity

Answer 10

If the production function is homothetic, the cost function can be written as C(p, y) = b(p) · a(y).

• Cost is proportional to output: a proportional increase in output requires the same proportional increase in inputs.
• changes in input proportions require only change in input scale

Question 11

long run costs: change of conditional inputs when input prices change

Answer 11

• ableitung von c nach pi ist zi (shephards lemma)
• two possible price changes:
  1) proportional change in input prices where all factor prices change in the same proportion
  2) non-proportionate change in input prices, only one price of an input increases

Question 12

long run costs: Effect of input price changes on total and average costs

Answer 12

Question 12

long run costs: Effect of input price changes on marginal costs

Answer 12

Question 12

Short-run cost

Answer 12

In the short run some inputs are fixed and cannot be adjusted. The existence of fixed input(s) is what defines the short run.
STC=LTC, wenn z2,0 =z2*

Question 13

Short-run cost minimization

Answer 13

Question 14

Short Term cost functions

Answer 14

SAC= STC/Q
S= FC+VC
AFC=FC/Q
AVC=VC/Q =SMC
SMC=STC Ableitung nach Q
SAC=AFC+AVC